calculate standard error from variance covariance matrix

The selection of the stepwise GWR method reduces several predictor variables that are not significant to the response variable. Yasin proposed the GWR stepwise method in order to choose a significant variable. The author discussed spatial analysis in detail by using OLS and estimator of spatial regression models with the maximum likelihood estimation (MLE) methods.

Spatial problems, specifically in parameter estimation has been studied by Cressie. According to, the GWR method is selected due to the weaknesses of the ordinary least square (OLS) parameter estimation results, where the variance error in the OLS model is still assumed to be fixed (homoscedasticity) and there is no dependency between errors (spatial effects) at each observation location. In statistical inference, estimation of spatial data parameters using the GWR approach has been carried out by many researchers. This study also provides researchers with an understanding of statistical inference procedures. This test uses a statistical inference procedure by reducing the MGWR model equation so that the estimated error variance-covariance parameters meet the characteristics of unbiased. The selection of the WLS method is based on the weighting function measured from the standard deviation of the distance vector between one observation location and another observation location. In this study, the estimated error variance-covariance parameters is obtained from the MGWR model using Maximum Likelihood Estimation (MLE) and Weighted Least Square (WLS) methods. The MGWR model is assumed to be an error vector that distributed as a multivariate normally with zero vector mean and variance-covariance matrix at each location, which is sized for samples at the -location. The Multivariate Geographically Weighted Regression (MGWR) model is a development of the Geographically Weighted Regression (GWR) model that takes into account spatial heterogeneity and autocorrelation error factors that are localized at each observation location.

Calculate standard error from variance covariance matrix